Google is aware of *anything* you put in the web. If it's linked to, Google will eventually get to it. If it's on your server, and you're not actively restricting access, Google will find it.
WordPress doesn't expose anything that you don't allow it to. If the site is coded to allow people to see the author's name and/or profile (and the info is in the public profile) then yes, Google will find it.
I think the best chance of discovering how Google has associated her name to the site is to find out who is linking to her site, and if they know her. You can look at the domain referers and see who's linking to her, or you can find links directly to her site by going to Google and putting in "link:www.domainname.com" (and other variations, using http: and no www) and anyone who's using that link on their site will come up.
But no, Google will see her public site and index it. Google can't see the admin area and index that - it's password protected (and Google can't get in password-protected areas). So she's either accidentally exposed herself on the site, or someone who knows who she is (and also knows it's her blog) has connected the two somewhere with a link. But WordPress doesn't "leak" any information that you don't allow it to.